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4 years ago

Solve for x Write the smaller solution first, and the larger solution second.

Mathematics

1 answer:

posledela4 years ago

6 0

Answer:

x= -18.16 x= -11.84

Step-by-step explanation:

(x+15)(x+15)= x^2+30x+225-10=0

x^2+30x+215=0

a=1 -30±√(30)²-4(1)(215)

b=30 -----------------------------

c=215 2(1)

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The Henley's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate

ella [17]

Interest paid after 30 years is $494,546.99.

Solution:

Principal (P) = $195,000

Interest rate (r) = 4.3%

Time (t) = 30 years

n = number of times interest calculated per year

n = 1

Compound interest formula:

$$A=P\left(1+\frac{r}{n}\right)^{n t}$

where A is the final amount

$$A=195000\left(1+\frac{4.3\%}{1}\right)^{1\times 30}$

$$A=195000\left(1+\frac{4.3}{100}\right)^{30}$

$$A=195000\left(\frac{100+4.3}{100}\right)^{30}$

$$A=195000\left(\frac{104.3}{100}\right)^{30}$

A = 689546.99

Interest = Amount - Principal

= 689546.99 - 195000

= 494546.99

Interest paid after 30 years is $494,546.99.

6 0

4 years ago

Evaluate the spherical coordinate integral

expeople1 [14]

Rewrite the equations of the given boundary lines:

y = -x + 1 ==> x + y = 1

y = -x + 4 ==> x + y = 4

y = 2x + 2 ==> -2x + y = 2

y = 2x + 5 ==> -2x + y = 5

This tells us the parallelogram in the x-y plane corresponds to the rectangle in the u-v plane with 1 ≤ u ≤ 4 and 2 ≤ v ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

$J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3$

Rewrite the integrand:

$-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3$

The integral is then

$\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}$

5 0

3 years ago

Sharon needs 64 credits to graduate from her community college. So far she has earned 56 credits. What percent of the required c

Anit [1.1K]

Sharon has a percentage of 56/64*100= 87.5%

3 0

3 years ago

Read 2 more answers

Factor the polynomial: 81b^2 - 64c^2

Lilit [14]

Answer:

160D^2

Step-by-step explanation:

5 0

3 years ago

A cylinder has a diameter of 10 units. Its radius is ____ units. Of its height is _______ twice its radius, its height is units.

SpyIntel [72]

Answer:

Height is 10 units

Volume is 785 cubic units

Step-by-step explanation:

We are given;

Diameter of a cylinder as 10 units

But, radius = d/2

= 5 units

Height is twice its radius,

Thus, Height = 10 units

We can get the volume;

Volume of a cylinder = pir²H

Taking pi to be 3.14

Then;

Volume = 3.14 × 5²× 10

= 785 cubic units

Thus, the volume of the cylinder is about 785 cubic units

6 0

3 years ago