the volume of a cube is 710 cm cubed work out the length of its side rounded to one decimal place​

Answer:

See solution below

Step-by-step explanation:

Given the expression

[tex]\frac{cos(x+30)-sin(x+60)}{sin(x)cos(x)} \\[/tex]

Recall that

cos x  = sin(90-x)

cos(x+30 ) = sin (90-(x+30)

= sin(90-x-30)

= sin(60-x)

Substitute

[tex]\frac{sin(60-x)-sin(x+60)}{sin(x)cos(x)} \\= \frac{sin60cosx-cos60sinx)-sinxcos60-cosxsin60)}{sin(x)cos(x)} \\= \frac{-2cos60sinx)}{sin(x)cos(x)} \\= \frac{-2(1/2)sinx)}{sin(x)cos(x)} \\= \frac{-1}{cos(x)}\\= \frac{1}{cos(x)}\\ \\= -sec(x) Proved[/tex]

Answer:

5

Step-by-step explanation:

what do you mean ?? its already written there

Answer:

The answer is 5

Step-by-step explanation:

The answer is 5 because the length across from the right angle is always the hypotenuse.

The maximum value of the function is 9/4.

The minimum value of the function is -1/4.

On the interval (0, pi/2), the function is strictly increasing.

The range of the function is [-1/4, 9/4].

Given function is:

[tex]y = \frac{5}{4} sin x +1[/tex]

The range of sin x is [-1, 1].

So the range of [tex]\frac{5}{4} sin x[/tex] will be [-5/4, 5/4]

So the range of [tex]\frac{5}{4} sin x +1[/tex] will be [-5/4 + 1, 5/4 +1]

The range of  [tex]\frac{5}{4} sin x +1[/tex] will be [-1/4, 9/4]

The maximum value of function = upper limit of the range of [tex]\frac{5}{4} sin x +1[/tex]

So, the maximum value of the function = 9/4

The minimum value of function = lower limit of the range of [tex]\frac{5}{4} sin x +1[/tex]

So, the minimum value of the function = -1/4

As we can see in the graph, in the interval (0, π/2) the function is strictly increasing.

Therefore, The maximum value of the function is 9/4.

The minimum value of the function is -1/4.

On the interval (0, pi/2), the function is increasing.

The range of the function is [-1/4, 9/4].

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Answer:

Complementary angles sum to 90°

Answer:

V = 226.19

Step-by-step explanation:

v=(Pi)(r^2)(h/3) = 3.14(6^2)(6/3) = 3.1415(36)(2) = 226.19

The closest to the volume of the cone is given by 226.19.

We have given that,

The radius of the base of a cone is 6 inches the height of the cone is 6 inches.

V=(Pi)(r^2)(h/3)

V= 3.14(6^2)(6/3)

V= 3.1415(36)(2)

V= 226.19

Therefore, The closest to the volume of the cone is given by 226.19.

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The total Amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.

a) The down payment of Jason is 10% of $430,000 =$43,000b) The amount of the mortgage is the difference between the home value and the down payment.

Mathematically, $430,000 - $43,000 = $387,000.c) The closing costs are 3.5% of the mortgage. So, 3.5% of $387,000 is: 0.035 × $387,000 = $13,545.

Hence, the closing costs are $13,545. d) The total amount of the mortgage if they finance the closing costs with the mortgage is the sum of the amount of mortgage and the closing cost.

So, the total amount of the mortgage is: $387,000 + $13,545 = $400,545.Solution:a) Jason's down payment is 10% of the cost of the house, which is given as $430,000.

To calculate the down payment, multiply the cost of the house by 10%.Down payment = $430,000 x 10% = $43,000

Therefore, Jason's down payment is $43,000.b)

The amount of the mortgage is the difference between the total cost of the house and the down payment. The cost of the house is given as $430,000.

Thus, we have:Mortgage amount = Total cost - Down paymentMortgage amount = $430,000 - $43,000Mortgage amount = $387,000

Therefore, the amount of the mortgage is $387,000.c) The closing costs are 3.5% of the mortgage.

Using the mortgage amount calculated in part b), we can compute the closing costs as follows:Closing costs = 3.5% x Mortgage amountClosing costs = 3.5% x $387,000

Closing costs = $13,545

Therefore, the closing costs are $13,545.

d) If the closing costs are financed with the mortgage, we simply need to add the closing costs to the mortgage amount calculated in part b):Total amount of the mortgage = Mortgage amount + Closing costsTotal amount of the mortgage = $387,000 + $13,545

Total amount of the mortgage = $400,545

Therefore, the total amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.

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Answer:

24

Step-by-step explanation:

Answer:

8 grams

Step-by-step explanation:

The half-life of a radioactive kind of krypton is 3 minutes. How much will be l6eft after 6 minutes, if you start with 32 grams of it?

The formula is given as

Nt = No(1/2) ^t/t½

Nt = 32 × (1/2) ^6/3

Nt = 8 grams

Answer:

Razones trigonométricas inversas: cosecante, secante y cotangente. ... Dado un triángulo rectángulo, definimos la cosecante, la secante y cotangente de un ángulo como las razones inversas del seno, coseno y tangente, respectivamente.

Step-by-step explanation:

espero y te ayude

Answer:

380

Step-by-step explanation:

280 coffe machine

15 bag multiple for 40= 600 - 15%= 540

540+280=820

1200-820=380

the answer tho this is that the tree is 14ft

Answer:

22.5

Step-by-step explanation:

20 ft for an 8 foot shadow but since you need 1 more foot

take half of 5 (2.5) and you get 22.5

Answer:

what do you need help with?

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

2:

# of sides = 3

# of vertices = 3

name of shape: triangle

3.

# of sides = 4

# of vertices = 4

name of shape: quadrilateral

4.

# of sides = 5

# of vertices = 5

name of shape: pentagon

5.

# of sides = 6

# of vertices = 6

name of shape: hexagon

6.

# of sides = 8

# of vertices = 8

name of shape: octagon

[tex] \tan(30) = \frac{x}{ \sqrt{72} } [/tex]

[tex] \sqrt{72} \tan(30) = x[/tex]

x equals about 4.9 rounded to the hundredths place.

Answer:

A)The angles in the smaller prism measure 90 degrees.

B)The perimeter of the rectangular bases changes by a factor of 2.  

E)The area of the rectangular bases changes by a factor of 4.

Step-by-step explanation:

The right rectangular prisms are similar.

Which statements are correct? Check all that apply.

A)The angles in the smaller prism measure 90 degrees.

B)The perimeter of the rectangular bases changes by a factor of 2.

C)The surface area changes by a factor of 8.

D)The larger prism has twice the volume of the smaller prism.

E)The area of the rectangular bases changes by a factor of 4.

Solution:

Two polygons are said to be similar if they have the same shape, the ratio of their sides are in the same proportion and they have the same size of angles.

A) Since the bigger prism has angles with measure of 90°, hence the angles in the smaller prism will also measure 90.

Option A is correct.

B) Perimeter of bigger prism base = 2(2.2 + 0.8) = 6

Perimeter of smaller prism base = 2(1.1 + 0.4) = 3

The perimeter of the rectangular bases changes by a factor of 2 (6 / 3).

Option B is correct.

C) Surface area of bigger prism = 2(3.2*0.8 + 2.2*0.8 + 3.2*2.2) = 22.72

Surface area of smaller prism = 2(1.6*0.4 + 1.1*0.4 + 1.6*1.1) = 5.68

The surface area does not change by a factor of 8 (22.72 / 5.68 ≠ 8)

Option C is wrong

D) Volume of bigger prism = 2.2 * 3.2 * 0.8 = 5.632

Volume of smaller prism = 1.1 * 1.6 * 0.4 = 0.704

The larger prism volume is not twice of the smaller prism

Option D is wrong

E) Area of bigger prism base = 2.2*0.8 = 1.76

Area of smaller prism base = 2.2*0.8 = 0.44

The area of the rectangular bases changes by a  factor of 4 (1.76 / 0.44 = 4)

Answer:

10 cm

Step-by-step explanation:

multiply first 4×2 which is Base. then multiply by 1 1/4 which is 10

Answer:

20%

Step-by-step explanation:

65 and 78 are both multiples of 13. Divide both by 13, we get 5 and 6.

If we use 5 as our main value (100%), 6 would be 120% as adding 1 to the main number (5) increases it by 20%. So 6 is a 20% increase from 5.

:D

Answer:

x = [tex]\frac{(a+b)}{2}[/tex]

[tex]y=\frac{a-b}{2}[/tex]

Step-by-step explanation:

System of equations has been given as,

x + y = a ----------(1)

x - y = b ---------(2)

By adding equation (1) and (2)

(x + y) + (x - y) = a + b

2x = a + b

x = [tex]\frac{(a+b)}{2}[/tex]

By substituting these values in equation (2),

x - y = b

[tex]\frac{a+b}{2}-y=b[/tex]

[tex]\frac{a+b}{2}-b=y[/tex]

[tex]\frac{a+b-2b}{2}=y[/tex]

[tex]\frac{a-b}{2}=y[/tex]

Answer:

a

Step-by-step explanation:

worng worng

Answer:

169 3/4 in³

Step-by-step explanation:

v=l×w×h

v=8× 1 3/4× 12 1/8

21  7/32×8= 169 3/4 in³

Answer:

7/25

Step-by-step explanation:

Answer:

That would seem like a b

Step by step explanation: (>) means greater than and b is stating that element a is higher than element c

Answer:

A, C, D

Step-by-step explanation:

42 + 14 = 56

38 + 18 = 56

67 + 33 = 100

70 + 30 = 100

93 + 35 = 128

95 + 33 = 128

B)

40 + 22 = 62

32 + 10 = 42

62 ≠ 42

2√3+6√2

hope this helps :D

Answer:

Step-by-step explanation:

2√3+6√2

Answer:

Short term Capital gain and $1200

Step-by-step explanation:

Any investment held under a year falls under short term capital gain

5,000 X 0.24 = 1,200

Answer:

Short term Capital gain and $1200.

Step-by-step explanation:

Gains earned by selling assets you’ve held for a year or less are called short-term capital gains, and they generally are taxed at the same rate as your ordinary income, anywhere from 10% to 37%.

Since Rita has a taxable income of $85,000.

So , she fall 24% 82,501 to 157,500 Tax rate bracket.

Therefore     5,000 X 0.24 = 1,200

Thus Rita must pay $1200 in taxes on the Short term Capital gain made by her.

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Answer:

133.33

Step-by-step explanation:

sorry if im incorrect

Answer:

800

Step-by-step explanation: