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3 years ago

The height of a triangle is 6 inches. The area of the triangle is 45 square inches. What is the length of the triangle’s base?

Mathematics

2 answers:

brilliants [131]3 years ago

6 0

Answer:

Step-by-step explanation:

A if Triangle= 0.5×(b×h)

0.5×(b×6)=45

b×6=45÷0.5

b×6=90

b=90/6=15

arlik [135]3 years ago

5 0

Answer:

15 in

Step-by-step explanation:

(basexheight)/2=area

basex6=45x2

base=45/3

base=15

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47.76 divided by 4.8

Vesna [10]

Answer:

the answer is 9.95

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3 years ago

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What is the volume of a cone (in cubic inches) with a radius of 6 inches and a height of 3 inches? Use 3.14 for pi. Round your a

Gre4nikov [31]

V = 1/3 * (pi) * r^2 * h
(pi) = 3.14
r = 6
h = 3

V = 1/3 * (3.14) * 6^2 * 3
V = 1/3 * 3.14 * 36 * 3
V = 1/3(339.12)
V = 339.12 / 3
V = 113.04 cubic inches <==

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3 years ago

Chloe drives from her house to her grandmas house 48 miles away in an hour and 12 minutes. How fast was she driving on average?

mestny [16]

Answer:

40 miles per hour

Step-by-step explanation:

change hours and minutes to hours

12 minutes = 12 minutes * 1 hr/ 60 minutes = 12/60 hrs

12/60 = 1/5 = .2 hours

1 hours 12 minutes = 1.2 hours

48 miles in 1.2 hours

48/1.2 = 40 miles/hour

5 0

3 years ago

Can somebody help me please

serious [3.7K]

Answer:

-7 and 21

Step-by-step explanation:

y-2y=7 (sub x=7 to the equation)

-y=7

y=-7 (not sure of its correct)

if y=-7,

x-2(-7)=7 (sub y=-7 into equation)

x-14=7

X=7+14

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8 0

3 years ago

Consider the differential equation x2y′′ − 9xy′ + 24y = 0; x4, x6, (0, [infinity]). Verify that the given functions form a funda

pantera1 [17]

Answer:

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

$y= c_1x^4+c_2x^6$

Step-by-step explanation:

Given equation is

$x^2y'' - 9xy+24y=0$

This Euler Cauchy type differential equation.

So, we can let

$y=x^m$

Differentiate with respect to x

$y'= mx^{m-1}$

Again differentiate with respect to x

$y''= m(m-1)x^{m-2}$

Putting the value of y, y' and y'' in the differential equation

$x^2m(m-1) x^{m-2} - 9 x m x^{m-1}+24x^m=0$

$\Rightarrow m(m-1)x^m-9mx^m+24x^m=0$

$\Rightarrow m^2-m-9m+24=0$

⇒m²-10m +24=0

⇒m²-6m -4m+24=0

⇒m(m-6)-4(m-6)=0

⇒(m-6)(m-4)=0

⇒m = 6,4

Therefore the auxiliary equation has two distinct and unequal root.

The general solution of this equation is

$y_1(x)=x^4$

and

$y_2(x)=x^6$

First we compute the Wronskian

$W(x)= \left|\begin{array}{cc}y_1(x)&y_2(x)\\y'_1(x)&y'_2(x)\end{array}\right|$

$= \left|\begin{array}{cc}x^4&x^6\\4x^3&6x^5\end{array}\right|$

=x⁴×6x⁵- x⁶×4x³

=6x⁹-4x⁹

=2x⁹

≠0

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

$y= c_1x^4+c_2x^6$

5 0

3 years ago